Maciek Klemm, Electromagnetics Group, Centre for Communications Research, University of Bristol
Ultra-wideband radar-based imaging system for breast cancer detection

8 Juin 2009, de 10h00 à 12h00, salle Galois Coriolis

In this talk we will present the microwave radar system developed for breast cancer imaging. During the past decade there has been a growing interest in application of microwave frequencies, between 3 and 10 GHz, to the medical imaging. Breast cancer imaging has been of the particular interest. Currently there are two main streams in microwave breast imaging: a) microwave tomography, b) radar-based imaging. Both approaches rely on a difference in the electrical properties of normal and malignant breast tissues. At the University of Bristol, we have focused our research efforts on the design of the ultra-wideband (UWB) radar-based imaging system for breast cancer detection. Our UWB radar system uses a hemi-spherical real aperture antenna array and a realistic 3D spherical breast phantom model, with electrical properties similar to real breast tissues. Our experimental system was built in such way that it can be used directly with real breast cancer patients. In this talk the development of this world's first operational breast imaging radar will be presented. Design details shown in the presentation will cover: UWB antenna design, full-wave electromagnetic modelling and signal processing. We will show some first prototypes, as well as the latest, fully operational system which has recently been used in the clinical trial in Frenchay Hospital in Bristol.

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Martin J. Gander, Université de Genève, Département de Mathématiques
Les méthodes multigrille: efficaces pour des problèmes diffusifs et difficilement utilisables pour la propagation d'ondes

2 Juillet 2009, de 10h00 à 12h00 (pause café de 10h45 à 11h15), salle Galois Coriolis

Les méthodes multigrilles ont été développées pour des problèmes diffusifs. Elles utilisent le fait que des méthodes itératives stationnaires comme Gauss-Seidel ou Jacobi avec un paramètre de relaxation sont efficaces pour éliminer des erreurs hautes fréquences, et qu'une grille fine n'est pas nécéssaire pour représenter des erreurs basses fréquences. Les méthodes multigrilles sont parmi les méthodes les plus efficaces qui existent pour des problèmes diffusifs, et des méthodes algébriques ont été construites avec une efficacité similaire pour le même type de problème.

Si on applique une méthode multigrille à un problème de Helmholtz, qui a comme seule différence un décalage dans le spectre qui conduit à un problème indéfini, on observe une convergence très lente et même une divergence de la méthode. J'expliquerai dans cet exposé les deux raisons principales qui expliquent cette perte d'efficacité et les modifications qui ont été proposées dans la littérature pour obtenir une méthode multigrille efficace pour des problèmes de Helmholtz, ainsi que deux idées plus récentes.

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Pavel Solin, Department of Mathematics and Statistics, University of Nevada, Reno (USA)
Solving multiphysics PDE problems with space-time adaptive hp-FEM on dynamical meshes

16 Juillet 2009, de 10h00 à 12h00 (pause café de 10h45 à 11h15), salle Galois Coriolis ou Euler Violet

Automatic mesh adaptation plays an increasingly important role in modern computational methods for PDE, and it will become their integral part eventually. The current state-of-the-art, however, is still far away from that. Nowadays, only adaptive low-order FEM for (some) stationary single-physics problems are mature enough. Regarding the rest, it is well known that adaptivity is more diffcult to handle for time-dependent problems than for stationary ones, that multiphysics PDE systems are more difficult to solve than single-physics equations, and that higher-order finite element methods (hp-FEM) pose more challenges than standard low-order FEM. Examples of time-dependent multiphysics PDE problems from various engineering areas will be used to illustrate main computational challenges. Using adaptive higher-order methods requires higher level of understanding of the underlying mathematics than low-order methods. We will show examples of elementary situations where newcomers are surprized and confused by not observing effects and improvements that they expected. We will explain why such behavior of higher-order methods is normal and what to do about it. We will also demonstrate that it is very advantageous to approximate various physical fields on individual meshes equipped with individual adaptivity mechanisms rather than on one common mesh, and our novel multimesh hp-FEM methodology for monolithic discretization of multiphysics PDE problems will be presented. A new class of space-time adaptivity algorithms on dynamical hp-meshes, obtained by combining the multimesh hp-FEM with the classical Roth method, will be discussed. We will discuss applications to several nonstationary multiphysics problems with amphasis on coupled problems related to electromagnetics fields.

Open Source project Hermes and some practical aspects of adaptive higher-order FEM

Hermes (HighER-order Modular finite Element System) is a C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers for single and multiphysics PDE problems. Hermes differs from most other adaptive FEM or hp-FEM codes through its flexibility. It is based on PDE-independent computational a-posteriori error estimates that make it possible to use automatic hp-adaptivity for any PDE or multiphysics PDE problem that can be solved using finite elements. It is the first software that came with space-time adaptive hp-FEM on dynamical meshes. We will discuss some aspects of design and implementation of adaptive higher-order finite element methods in Hermes, discuss the roles of C++ and Python in the software development, and show an interactive web portal which allows you to use Hermes from a PDA or iphone.

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Jan S Hesthaven, Division of Applied Mathematics Brown University, Providence (USA)
Accelerating high-order accurate computational methods for solving PDE's

22 Juillet 2009, de 10h30 à 12h00, salle Galois Coriolis ou Euler Violet

High-order accurate computational methods for the numerical solution of partial differential equations have enjoyed considerable success and continue to grow in use with the increasing emphasis on accuracy and long term integration in large scale complex applications. However, the computational cost of these techniques continues to be a criticism raised against these methods. This perception limits their use in large scale production and industrial settings where the use of large distributed-memory parallel computing platforms often are not desirable.

In this talk we discuss three different approaches to address this concern. In the first part, we introduce a new familiy of orthogonal functions which are particularly well suited for representing problems on unbounded domains. The functions are Fourier like but are much more flexible in terms of application. We shall demonstrate their use on wave- and plasma physics problems.

In the second part, we address another challenge associated with small time-steps and consider local time-stepping techniques in connection with discontinuous Galerkin methods. We shall discuss different techniques and illustrate the advantages of such methods for electromagnetic and plasma-physics applications.

In the last part, we discuss recent studies of the use of graphics processing units (GPUs) as a way to accelerate large scale applications solved using discontinuous Galerkin methods. We shall observe that a central property that enables the use of the GPU is that the majority of DG operators are applied in an element-local way, with weak penalty-based element-to-element coupling. This locality in memory access is a key enabling factor that allows DG to run efficiently on off-the-shelf, massively parallel GPU's. Example computations achieve and surpass 700 gigaflop/s of net application-level floating point work. It is noteworthy that the maximum acceleration is achieved at orders of approximation of three to five as these are generally thought to be of most relevance for industrial applications.

This work is done in collaboration with Tim Warburton (Rice), Andreas Kloeckner (Brown), Akil Narayan (Brown), and Nico Godel (Hamburg).

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